


A Treatise on Binomial Theory

by JadeRachelle



Category: Sherlock (TV), Sherlock Holmes & Related Fandoms, Sherlock Holmes - Arthur Conan Doyle
Genre: M/M, Masturbation, Mathematics, Oral Sex
Language: English
Status: Completed
Published: 2013-09-22
Updated: 2013-09-22
Packaged: 2017-12-27 07:47:08
Rating: Explicit
Warnings: Creator Chose Not To Use Archive Warnings, No Archive Warnings Apply
Chapters: 1
Words: 3,249
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/976258
Author URL: https://archiveofourown.org/users/JadeRachelle/pseuds/JadeRachelle
Summary: <blockquote class="userstuff">
              <p>For dynamics-of-an-asteroid on tumblr.<br/>Jim wants something a little more from his odd partnership with Sherlock but isn't entirely sure how to get him to give it up. This is how he finds out exactly what to say to get the detective going.</p>
            </blockquote>





	A Treatise on Binomial Theory

**Author's Note:**

> I used a few ACD references in this - namely Jim's past work as the chairman of mathematics at 'a small university' (often assumed to be Leeds), his status as a professor and his past papers/publications (Dynamics of an Asteroid and a discourse on binomial theorem.)
> 
> I actually don't know anything about binomial theorem so kindly ignore all inaccuracies. I did a few hours of reading on it but a lot of it went over my head. I never was one for maths unless I worked very hard at it.
> 
> Uh, also... in case you were wondering...
> 
> Sapiosexual is one who is stimulated and aroused physically by intelligence and the proof of such. I see Sherlock as a sapiosexual, he would be turned on by logic, science, intellect and it's implications. Having someone show off their intelligence would get him off. Once his mind is stimulated, the body follows. Yes?

Jim sat staring at the laptop screen blankly. There was nothing more to do. He had appeased all clients, set all plans into action, pulled all threads and set up all that was needed. He rarely found respite with work, constantly receiving new clients, new plans, new buyers, new requests. When there was a lax in work he would usually turn to his pet project and set up puzzles for his favourite detective but there was really no point when said detective was currently lounging on the couch behind him less than three metres away. Jim leant backwards in his chair and tilted his head to look at the man. He was slumped over the velvet cushions, legs crossed at the ankle and arms above his head stretched straight out like a cat. He was dressed haphazardly in a blue silk robe, a t shirt and a pair of soft pajama bottoms despite the fact that he was essentially a guest in this flat and it was well into the late afternoon. Jim watched him for a minute, unmoving, unspeaking, Sherlock simply lay still, obviously thinking.  
  
That was the thing with Sherlock, if he was deep in thought you couldn't rouse him to speak or act. His reactions were limited and often quite frustrating with their sporadic appearance. It was one thing to refuse physical interaction in this relationship - something that irritated Jim intensely, but it was quite another to refuse even social interaction such as conversation. It seemed that while Sherlock had indeed proposed they enter a relationship together, he hadn't been prepared to actually act as though he were a partner to Jim. There was the undeniable comfort of having the detective physically present in his flat, watching him think and sleep and stare at Jim as he worked but it lacked authenticity. The distinct rarity that was physical contact - only ever begun by Jim himself, was something that set him on edge. While Sherlock may have had no interest in moving beyond the endured press of lips Jim forced upon him, the criminal was certainly interested in more.  
  
He had tried numerous things to get the detective 'in the mood' but nothing had worked. Not the demanding, the pleading, the trickery, the attempted sedation, the failure that was seduction and the straight up embarrassing attempt at simply stripping and lounging around hoping to catch his eye.  
  
He knew very well that no matter how much the detective tried to convince him he was asexual, he couldn't deny that he had been caught out a few times with physical proof of arousal, generally when reading or watching Jim work. There was obviously something that stimulated his body, Jim just had yet to find it and manipulate it to his advantage.  
  
He watched as Sherlock sighed deeply, his eyes closed and fingers tapping against the arm rest slightly.  
  
"Are you just going to sit there and stare at me?" he drawled.  
  
Jim scowled and looked back at his computer screen.  
  
"Well there's nothing else to do. You won't talk to me or let me touch you." he replied sourly.  
  
"Doesn't mean you have to be silent and grumpy." the detective said in an airy tone of nonchalance.  
  
"Oh, shall I just sit here and talk to you then? Talking at you, about... Bollocks like my book or discourse or something?"  
  
Sherlock shrugged noncommitally, "if you like. I wouldn't mind hearing you talk."  
  
Jim sighed and turned to face the tall man with a raised eyebrow.  
  
"Shall I come over there to talk to you or would you prefer your space?"  
  
He was met with another shrug. Sherlock was clearly not in the worst mood possible and Jim would take advantage of that. He stood up and wandered the few feet to the sofa, moving to straddle Sherlock's thighs awkwardly.  
  
"Must you sit right there?" the detective asked as he cracked one eye lazily.  
  
Jim shrugged and shifted to get comfortable.  
  
"Where shall I start?" he asked looking down at the detective, "have you read my book?" he asked.  
  
"Didn't realise you had one." Sherlock said blandly as he closed his eyes again.  
  
"I do, yes. Published and accredited. From when I was teaching."  
  
"You taught?"  
  
"Professor in advanced mathematics and theoretical physics."  
  
"What's it called?"  
  
"Dynamics of an Asteroid. But no one has ever criticised it, no one can review it. When they try, they simply state that the mathematics are so esoteric they don't know where to start, what to begin with, if they really understood it or not."  
  
Sherlock lay silent for a moment under Jim, not moving or speaking, only his chest rising and falling before the criminal.  
  
"What about the discourse?" the detective asked eventually.  
  
"A Treatise on the Binomial Theorem," Jim replied, "I was twenty one when I wrote it. I'd been in England for six months. It won me the mathematical chair at Leeds University. You really haven't researched me have you? There's photos and everything, darling. Year books, awards, records, papers..." he tutted in a disappointment, "I'm a little hurt that you didn't dig into my past."  
  
Sherlock rolled his eyes and shifted his hips slightly to relieve the weight of Jim on his lap.  
  
"Are you going to tell me about it or not?" he asked with a raised eyebrow, "Come on. Impress me. I know you love to show off your intellect."  
  
Jim placed his hands on Sherlock's chest with a slight frown, "you only know that because you're the same. But yes. Do you know much of the binomial theorem?"  
  
Sherlock lifted one shoulder in a shrug that suggested he knew a little but obviously not as much as the man on top of him.  
  
Jim smiled and immediately launched into an explanation.  
  
"In mathematics there is a name for expressions constructed from variables and constants using only addition, subtraction, multiplication and non-negative integer exponents - polynomial. Two polynomial terms together bound by parentheses is known as a binomial. The binomial theorem describes the algebraic expansion of the - you know what an exponentiation operation is?"  
  
Sherlock nodded, both eyes focused on Jim as he spoke as though he were telling the most fascinating tale one could imagine.  
  
"Right. The theorem describes the algebraic expansion of the powers of a binomial. It makes it possible to expand the power into a sum where both exponents are non-negative integers and the coefficient of each is a positive integer. The coefficients can be arranged to form Pascal's Triangle and the formula is often written using summation notation.  
  
My discourse was an expansion on Newton's generalised binomial theorem and the importance of the replacement of finite with infinite series to give meaning to coefficients with an arbitrary upper index in relation to generalised hypergeometric functions. Newton's generalisation allowed real exponents other than non-negative integers. By swapping out the finite for infinite, one must factor out parenthesis n minus k parenthesis factorial from numerator and denominator in the formula and replace n by r which would then stand for an arbitrary number..."  
  
Jim trailed off as Sherlock shifted beneath him, his mouth slightly open and stare focused intensely on his face. Jim raised one hand and ran it through his hair, a little confused at the expression that had leaked onto the detective's face.  
  
"Am I making any sense? Shall I stop before I bore you to death?" he asked Sherlock.  
  
The detective shook his head, eyes not leaving Jim's face as he moved his hands to rest on Jim's hips. The criminal furrowed his brow and glanced down at the contact with a tilt of his head. He dropped his hand again to rest of Sherlock's chest and continued with a smirk.  
  
"When one uses Newton's theorem one can define parenthesis r k equaling r close r minus one parenthesis falling factorial close r minus k plus one close over k factorial equaling parenthesis r close k over k factor-"  
Jim stopped his listing of the equation as he felt Sherlock's hips shift again and glanced down. With a grin he noticed that the grip on his hips had increased and the shift had been Sherlock pushing his hips up to meet Jim's own. The detective's pajama bottoms were filled out with the obvious shape of an erection and Jim almost laughed.  
  
So he had finally discovered what it was that stimulated Sherlock. He should have known it earlier, it was glaringly obvious now that he thought about it.  
  
"Asexual my arse," Jim said as he grinned down at Sherlock, "fecking sapiosexual. I should have got that sooner."  
  
"Shut up," the detective hissed, "just... just talk okay?"  
  
Jim cocked an eyebrow, "darling, you are a contradiction and a half. Do I close my mouth or do I continue? Make up your mind."  
  
"Continue."  
  
Jim moved to settle himself over Sherlock's lap, his own groin now flush against the detective's growing erection and continued to speak. Although he had no doubt that Sherlock was most likely not following along completely he was sure that he was enjoying the equations and explanations. It seemed the man was aroused by intelligence itself and the expressing of such intellect, no matter the branched subject.  
  
"Where was I? Oh, yes. If one were to rewrite it using the Pochhammer symbol for the falling factorial and having x and y as real numbers with single vertical x greater than single vertical y and r as any complex number, one would have the equation parenthesis x plus y close power to r equaling infinite sigma of k equaling zero parenthesis r k close x to power of r minus k and y to the power of k..."  
  
Jim rocked his hips forward against Sherlock, earning him a slight hiss as the detective inhaled sharply. This was certainly no problem. He was getting what he wanted. He was getting to arouse Sherlock and the fact that he was doing so simply by showing off his intellectual prowess was enough to rouse him to stimulation as well. He ground his hips against Sherlock as he continued to speak, lowering his voice slightly and moving in a rocking motion as he trailed his fingers over the man's chest.  
  
"...equaling x to the power of r plus x r to the power of r minus one and y plus r parenthesis r minus one close over two factorial..."  
  
He slipped his hands under the hem of Sherlock's thin t shirt and raked his nails across his skin earning him a slight moan as he continued his movement and words with a smirk.  
  
"x to r minus two and y to two plus r parenthesis r minus one close..."  
  
He felt himself harden as Sherlock dug his fingers into his hips, pulling him down hard against the detective's erection impatiently but continued to speak.  
  
"parenthesis r minus two close over three factorial x to r minus three and y to three plus falling factorial..."  
  
Jim let his hands wander down to slip over Sherlock's hips, fingers skimming the waistband of his pajamas as he ground against him seeking friction.  
  
"R is the nonnegative integer, darling. At most r plus one nonzero term. Other values have infinitely many nonzero terms if x and y are nonzero. When one is working with infinite series from Newton one represents them in terms of generalised hypergeometric functions."  
  
He slipped his hands into Sherlock's pajamas and shimmied so that he was once again sitting on his thighs. He wrapped his fingers around the detective's length, closing his eyes at the feel of the warm flesh in his hand finally. He had wanted this for a long time and he had finally figured out how to make it enjoyable for Sherlock. Any longer and he would have gone mental, thankfully he had discovered exactly what to say to get Sherlock going, even if it was rather unconventional.  
  
"Taking r equaling minus s gets you a useful formula. Would you like to hear it?" he said as he opened his eyes and looked down again at Sherlock's face. His eyes were heavily lidded, mouth slightly open as his breathing came out laboured, hands still gripping Jim's hips. He nodded and licked his lips and Jim bit his tongue for a moment to stop himself from giggling at his success.  
  
"One over parenthesis one minus x close to s equaling infinite sigma of k equaling zero and parenthesis s plus k minus one of k close x to k to the equivalence of infinite sigma of k equaling zero and parenthesis s plus k minus one of s minus one close x to k with s equaling one yielding the geometric series formula."  
  
He began to lightly stroke the detective, fingers moving to apply pressure on each upstroke. He flicked his wrist and earned himself a breathless moan from Sherlock and made his hips buck. He paused to raise himself off of his lap and pull down the pajamas, freeing Sherlock from the confines of the thin fabric for Jim to study. He smiled widely to himself and pushed at Sherlock's legs to make him move up to make room for him on the relatively small couch. The man did as he was urged and Jim pulled the detective's trousers off completely, happy that the man was comfortable enough to go without pants with his pajamas. Jim took him in hand again, moving to settle himself between the man's thighs and continue his mathematical explanations.  
  
"When one is dealing with complex numbers in the binomial theorem one can combine it with De Moivre's formula. That is, the formula that any complex number x and integer n holds that the equation would be parenthesis cos x plus i sine x close to the power of n equaling cos parenthesis n x close plus i sin parenthesis n x close with i standing in for the imaginary unit parenthesis i squared equaling minus one close."  
  
Jim lowered himself to press a kiss to Sherlock's thigh lightly, hand slowly returning to its earlier pace along his shaft as he smiled to himself, proud of having finally managed to stimulate the man.  
  
"However," he stated between trailing kissed along Sherlock's leg to his hip, "De Moivre does not hold for non-integer powers due to their powers of complex numbers having so many different values. When the formula is combined with binomial theorem it yields multiple angle formulas for the sine and cosine."  
  
Jim placed a sharp bite on Sherlock's thigh, soothing it with his tongue before continuing with his mathematical monologue, his hand still working at a teasing pace along Sherlock's cock.  
  
"According to De Moivre, cos parenthesis n x close plus i sin parenthesis n x close equals parenthesis cos x plus i son x close to n. With the theorem I wrote of, the expression can be expanded, real and imaginary parts taken to yield formulas for cox nx and sin nx."  
  
He felt Sherlock's hands move to settle in his hair, his entire body trembling with want as Jim spoke, the equations and numerals acting as a stimulant much like the simple provocative 'dirty' talk of a conventional man's bedroom would. Jim let out a soft chuckle and licked a stripe up Sherlock's erection from base to tip, solid, slow, still teasing. He heard the man moan and felt the fingers tighten in his hair but pulled back slightly and continued his speaking.  
  
"This would, in general, by passing the double angle identities, be cos parenthesis n x close equaling sigma of k even parenthesis minus one close to k divided by two parenthesis n and k close cos to n minus k and x sin to k and x."  
  
He paused to shift and tentatively touch his tongue to Sherlock's head, tasting the small amount of precome that had gathered as he had spoke. Sherlock's tugged at his hair forcefully, trying to drag him closer to create more contact. Jim pressed his lips to the tip of Sherlock's cock and mumbled against it with a smirk.  
  
"Do you want me to shut up, now?" he teased as he let one hand move down to his own erection to palm himself through his trousers. Sherlock replied with an impatient sigh, "yes."  
  
As though he had been waiting for permission from the detective, Jim fumbled with his belt as he stretched his lips over Sherlock's length, taking just the head into his mouth and sucking lightly. He ripped his own fly open and unceremoniously shoved his hand into his pants to take hold of himself. He knew that even if Sherlock had been turned on by the example of intellect he had shown and was allowing Jim to touch him, he would be hard pressed to return the favour. He had no problem with managing himself as long as he got to touch Sherlock and watch him come undone.  
  
Jim steadied Sherlock's cock with one hand as he moved to take more into his mouth, his tongue lapping and cheeks hollowing as he applied pressure and bobbed. Sherlock's fingers pulled at his hair, urging him on as the man gasped and moaned with pleasure. Jim shut his eyes tightly as he began to stroke himself in time with his jaw movements, craving release of his own but needing to bring Sherlock to orgasm before he took care of himself. He shifted, hand uncomfortably rubbing against the inside of his pants as he gripped himself harder. He let Sherlock guide his movements with his hands and moaned around the man's cock as he felt the detective's hips begin to buck as he lost himself in the sensation.  
  
Jim opened his eyes and looked up at Sherlock and almost choked. He was taken aback by how completely open the man currently looked; arms stretched down to hold Jim's head, hips pumping slightly, head thrown back, neck exposed as he panted and bit his lip. Jim stopped the movement of his own hand on himself lest he lose himself before finishing his partner. He worked Sherlock with a fierce determination, tongue lapping and cheeks beginning to ache as he let Sherlock pump into his mouth wantonly. As he felt the thighs on either side of him tense he returned to touching himself, aching for release with harsh, quick strokes. He heard the detective utter a string of curses under his breath before his entire body went rigid, fingers ripping at Jim's hair as he pushed himself into Jim's mouth. The criminal felt Sherlock's release coat the back of his throat; warm and pumping as it filled his mouth. The knowledge that he had just driven Sherlock to orgasm pushed him over the edge, his own muscles clenching as he felt his climax rip through him. He swallowed deeply around Sherlock's cock as they both shuddered, feeling his own come dampen his hand and pants as he squeezed his eyes shut and dragged Sherlock's orgasm out as long as possible.  
  
He felt the hands on his head grow limp and slide from his hair as he moved to sit up wiping at his mouth with his free hand. He withdrew his other from his pants, holding up his fingers now coated with his own release to show the detective. He let a grin spread across his face lazily and leant against the armrest of the sofa in exhaustion.  
  
"Guess I should talk to you about my work more often."

  



End file.
